Sure, here's an example of how you could implement this in Kivy using Python:

```python
from kivy.app import App
from kivy.uix.widget import Widget
from kivy.graphics import Color, Ellipse
from kivy.clock import Clock
from random import randint

class Particle(Widget):
    velocity_x = 0
    velocity_y = 0
    lifespan = 100
    
    def move(self):
        self.pos = (self.pos[0] + self.velocity_x, self.pos[1] + self.velocity_y)
        self.lifespan -= 1

class Game(Widget):
    particles = []
    
    def on_touch_down(self, touch):
        for i in range(randint(10, 20)):
            particle = Particle()
            particle.pos = touch.pos
            particle.velocity_x = randint(-10, 10)
            particle.velocity_y = randint(-10, 10)
            self.particles.append(particle)
            self.add_widget(particle)
        
    def update(self, dt):
        for particle in self.particles:
            particle.move()
            if particle.lifespan <= 0:
                self.remove_widget(particle)
                self.particles.remove(particle)
        
class MyApp(App):
    def build(self):
        game = Game()
        Clock.schedule_interval(game.update, 1.0/60.0)
        return game

if __name__ == '__main__':
    MyApp().run()
```

This code creates a Particle class that represents the circles that will be created on click, and a Game class that holds a list of particles and updates their positions every frame.

When the user clicks, a loop is used to create a random number of particles at the click position with random velocities. The Game class's update method is scheduled to be called every frame using Clock.schedule_interval, and it updates the position of each particle, removes any particles that have run out of lifespan, and removes them from the screen.

To run the app, you can save this code to a file called main.py and run it with python main.py in a terminal.
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